Math Monthly Podcast

Follow along as I write and publish two lessons for the Math Monthly Journal. In Lesson 2, I transpose a 3D column vector and use Einstein summation to write the resulting row vector. In Lesson 3, I expand the dot product of a vector with itself and show why the six cross terms vanish, leaving the sum of the squared components.

You’ll also see how I turn my Microsoft Word notes into web lessons and organize the videos and derivations in the lesson library. These examples lay the groundwork for tensor analysis in physics and engineering.

Ex...

Why does the assigned textbook matter so much in a STEM course? I explain how definitions, notation, and worked examples give you a framework for solving problems independently. A symbol’s meaning can change from one book to the next, and even boldface or italics can affect how you read an equation.

I also explain how typing out complete solutions helps you practice a skill you’ll use beyond college: documenting your reasoning clearly enough for someone else to follow and check your work.

Find more college study tips from Author Jonathan David at

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A student asked me whether she should pursue pharmacy or engineering. In this episode of Tips & Tricks for College PLEM Majors, I share how studying physics and engineering led me toward mathematics and theoretical physics, and what I wish I’d asked before choosing a major.

What parts of the coursework do you enjoy enough to keep exploring? What does a typical workday look like in each field? I talk about using your early courses to test your interests and asking working pharmacists and engineers what they actually do day to day.

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What’s different about an engineering course that combines linear algebra and differential equations? In this Math Monthly podcast, Author Jonathan David introduces the crash course and explains why the assigned textbook’s notation and methods matter when you write a solution.

The episode revisits a matrix exponential problem using Jordan form. A ChatGPT response meant to mimic Maple used the opposite change-of-basis convention from the textbook. The example shows why checking how the book defines P can help you catch a sign error before it carries through the calculation.

Jonathan also reflects on his expe...

Create an organized, clickable image library on your WordPress website.

In this PLEM Academy miscellaneous lesson, Professor Jonathan D. Tullis demonstrates how he arranges book covers in columns and links them to individual lesson-library pages.

Follow along as he builds the layout, prepares cover images in Canva, and connects each image to its corresponding page.

In this walkthrough:

• Prepare and name book-cover images before uploading.• Add images to columns and create additional rows.• Create destination pages for individual lesson libraries.• Add introductory HTML headers and featured images.• Hyperlink cover images to the approp...

Start building a professional website for your resume, textbook, and project portfolio by choosing your web hosting and domain name.

In the first Building Your Website lesson, Professor Jonathan D. Tullis walks through his preferred GoDaddy hosting setup and explains why he uses cPanel-based web hosting for his WordPress website.

In this lesson:

• Explore the hosting options shown in the demonstration.• Understand Professor Tullis’s preference for cPanel-based hosting.• Compare monthly payments with longer introductory billing terms.• Consider renewal costs and optional services before purchasing.• Choose a professional domain name for your resume and portfoli...

Start writing your own textbook with an organized Microsoft Word document designed for print.

In the first Writing Your Book lesson, Professor Jonathan D. Tullis demonstrates how he prepares a reusable manuscript document for his career-focused book, How to Get a Job at NASA Before You Graduate.

Follow along as he sets up the document’s layout, styles, front matter, and navigation before beginning the writing process.

In this lesson:

• Organize your book’s folders and individual document files.• Set up an 8.5 × 11-inch textbook layout.• Adjust inside and outside margins for binding.• M...

Learn how to use AI to organize and present your original work while building a professional WordPress portfolio.

In this first PLEM Academy miscellaneous lesson, Professor Jonathan D. Tullis demonstrates his workflow for creating the program’s branding, organizing lesson libraries, and publishing video content on WordPress.

Follow the process as he uses ChatGPT to create supporting graphics and HTML layouts while keeping his own recorded lessons and experience at the center of the content.

In this walkthrough:

• Establish a consistent color scheme and visual identity.• Create certificate artwork, thumbnails, and lesson...

Turn your college education into a textbook, a professional website, and a portfolio that shows employers what you can do.

In this introductory podcast, Professor Jonathan D. Tullis explains the PLEM Academy Resume Building Certificate program—a guided, self-paced approach to developing career skills while working toward your degree.

The goal is to write your own career-focused textbook while documenting the skills, projects, and experience behind your resume. Begin with job postings that interest you, identify the tools employers request, and build those skills into your educational work.

Explore how to:

• Writ...

This Is How to Build Your Resume and Digital Portfolio While in College

Explore my resume-building program, designed to help you develop practical skills and document your accomplishments before graduation.

• Build a professional WordPress website to showcase your resume.• Learn the basics of HTML, website hosting, and cPanel.• Use ChatGPT to assist with HTML and website development.• Strengthen your Microsoft Office skills through practical work.• Create a portfolio of selected coursework, projects, and technical documents.• Screen-record your work to demonstrate your process and software skills.• Practice clear written and oral communication by presenting your projects.• Organize and sto...

This Is Why Index Notation Comes Before Tensor Analysis - Math Monthly Research

Discover how our live research group will explore index notation, build toward tensor analysis, and practice writing professional mathematical documents using Mary Boas’s textbook.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

https://MathMonthly.com

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This Is How Index Notation Works - Vectors and Einstein Summation Convention - Part 1

Learn how sequences, vector components, and basis vectors introduce index notation and Einstein summation convention in preparation for tensor analysis.

Textbook reference: Mary L. Boas, Mathematical Methods in the Physical Sciences, 3rd edition, Wiley.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

https://MathMonthly.com

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Explore Mary L. Boas’s Mathematical Methods in the Physical Sciences as we introduce Cartesian tensors, index notation, and Einstein summation convention for Math Monthly’s engineering focus.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

https://MathMonthly.com

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This Is How Math Monthly Works - Memberships, Live Research, and Your Questions

Explore Math Monthly’s membership options for digital lessons, podcast and textbook requests, live group research, and a signed monthly journal mailed to you.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

https://MathMonthly.com

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This Is What My How to Study Guide Looks Like - For STEM Majors Taking Calculus

Look inside my How to Study in College guide for textbook note-taking examples, mathematical solution writing, exam strategies, and preparation for professional work.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

https://MathMonthly.com

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This Is How to Study From a Textbook Before College Classes Begin

Learn my approach to reading ahead, organizing definitions and formulas in Microsoft Word, and practicing textbook examples independently.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

https://MathMonthly.com

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Why STEM Majors Need to Read the Textbook - Study Habits and Academic Integrity

My perspective on using your assigned textbook, following your syllabus, and building independent study skills for college and employment.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

https://MathMonthly.com

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Why I Left Wyzant Tutoring - My Experience and Lessons on Independent Study

I reflect on my years tutoring through Wyzant, why I left, and how those experiences shaped my views on academic integrity and independent textbook study.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

https://MathMonthly.com

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Integral Test - Does ∑ 1/(n ln n) Converge or Diverge?

Apply the integral test to ∑ₙ₌₂∞ 1/(n ln n), checking continuity, positivity, and decreasing behavior before evaluating the improper integral.

Textbook reference: James Stewart, Calculus: Early Transcendentals, 8th edition, Cengage Learning, Section 11.3, Exercise 21.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

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Geometric Series - Convergence and Finding the Sum - Calculus Crash Course

Determine whether ∑ₙ₌₁∞ (−3)ⁿ⁻¹/4ⁿ converges and find its sum by identifying the first term, common ratio, and geometric series formula.

Textbook reference: James Stewart, Calculus: Early Transcendentals, 8th edition, Cengage Learning, Section 11.2, Exercise 23.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

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Sequences and Series - Calculus Crash Course Introduction

Review sequences, series, and convergence tests in Stewart’s Calculus, with an emphasis on stating theorems, checking conditions, and writing complete solutions.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at https://MathMonthly.com.

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Inside Before Starting Physics - Math Preparation and Problem Solving

Look inside my Before Starting Physics guide for study advice, algebra and calculus preparation, and examples of how to approach physics problems.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

https://MathMonthly.com

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Explore my books and PDF bundle, which include access to a library of lessons. If you purchase a hardcover, send me your purchase receipt to receive the PDFs and lesson library access.

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Inside The Ultimate Cheat Sheet - Math Formulas, Tips, and Worked Examples

Preview my formula guides covering algebra, trigonometry, calculus, differential equations, linear algebra, and basic physics, with tips and examples written from a student’s perspective.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

https://MathMonthly.com

.

Explore my books and PDF bundle, which include access to a library of lessons. If you purchase a hardcover, send me your purchase receipt to receive the PDFs and lesson library access.

Tr...

Inside The Ultimate Crash Course for STEM Majors - Algebra, Calculus, and Beyond

Take a look inside my Ultimate Crash Course, featuring detailed solutions written from a student’s perspective, from algebra and calculus through introductions to vectors, physics, and tensor notation.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

https://MathMonthly.com

.

Explore my books and PDF bundle, which include access to a library of lessons. If you purchase a hardcover, send me your purchase receipt to receive the PDFs and...

Before Starting Physics - Study Skills, Math Preparation, and Problem Solving

Explore my Before Starting Physics guide, covering algebra and trigonometry preparation, algebra-based versus calculus-based physics, and how to structure solutions.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

https://MathMonthly.com

.

Explore my books and PDF bundle, which include access to a library of lessons. If you purchase a hardcover, send me your purchase receipt to receive the PDFs and lesson library access.

Triple Play PDF Bundlehttps://payhip.co...

The Ultimate Cheat Sheet - A Formula Guide for STEM Majors

Explore my Ultimate Cheat Sheet, combining study guidance, essential formulas, and explanations from algebra through calculus, linear algebra, differential equations, and basic physics.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

https://MathMonthly.com

.

Explore my books and PDF bundle, which include access to a library of lessons. If you purchase a hardcover, send me your purchase receipt to receive the PDFs and lesson library access.

Triple Play PD...

The Ultimate Crash Course for STEM Majors - What’s Inside and Which Edition to Choose

Discover why I wrote the Ultimate Crash Course, how it covers algebra through calculus and introduces advanced topics, and which edition fits your studies.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

https://MathMonthly.com

.

Explore my books and PDF bundle, which include access to a library of lessons. If you purchase a hardcover, send me your purchase receipt to receive the PDFs and lesson libr...

Cooking Show Update - Math Monthly and December Linear Algebra

An update on my month-long cooking show break, changes to live chat, and December’s linear algebra focus for Math Monthly.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

https://MathMonthly.com

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Explore my books and PDF bundle, which include access to a library of lessons; if you purchase a hardcover, send me your purchase receipt to receive lesson library access.

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Differential Equations and Linear Algebra - Textbook Review for Science and Engineering

A review of Grant Gustafson’s textbook, exploring engineering applications, computer-assisted solutions, and the detailed work behind textbook examples.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

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Explore this month’s engineering focus through collaborative math and physics problems, textbook navigation, and clearly written solutions.

If you’re a PLEM enthusiast interested in math, physics, or engineering, join Math Monthly at

https://MathMonthly.com

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The Difference Between Taking Physics in College and Actually Understanding It

Welcome to Professor Jonathan D. Tullis. Explore the difference between completing physics coursework and developing an understanding of the concepts, mathematical reasoning, assumptions, and applications behind the equations.

Join the research group at https://mathmonthly.com and explore membership options for live sessions, recordings, monthly PDFs, and mailed journals.

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Math Monthly Research Recap | Matrix Exponentials, Picard Iteration, and Maple

Welcome to Professor Jonathan D. Tullis. This recap reviews our Math Monthly research group session using Volume II of Gustafson’s Differential Equations and Linear Algebra, covering systems of differential equations, matrix exponentials, Picard iteration, and Jordan form.

We discuss navigating the textbook’s definitions and theorems, exploring Maple code through an AI simulation, and identifying a matrix-inverse error. The session emphasizes careful reasoning, writing formulas explicitly, and verifying results through the “full circle of math.”

Members can continue the discussion online, share their wo...

Adults Returning to College | Learning Math and Physics with Math Monthly

Welcome to Author Jonathan David. Returning to college as an adult? Discover my approach to textbook study, clear mathematical solutions, and verifying answers through the “full circle of math.”

Learn how Math Monthly combines live group sessions across algebra, calculus, linear algebra, differential equations, and physics with a monthly journal documenting our work. I also discuss plans for collaborative research and acknowledging members’ contributions.

Become a member at https://mathmonthly.com to join live Zoom sessions for Q&A, guidance, and participation. Sessio...

Adults Returning to College Are the Future of STEM

Welcome to Author Jonathan David. Drawing on my experiences as an adult student and longtime private tutor, I discuss why I’m shifting my focus toward adults returning to college and adults interested in learning mathematics and physics.

Topics include persistence, independent study, textbook reading, and approaching a demanding STEM education with experience and purpose.

Become a member at https://mathmonthly.com to join live Zoom sessions for Q&A, guidance, and research discussions. Explore membership options for digital access and monthly PDF or ph...

How to Learn Math as an Adult | Math Monthly with Jonathan David

Welcome to Author Jonathan David. Discover my approach to learning mathematics as an adult: start with algebra fundamentals, read methodically, develop reusable problem-solving methods, and verify your results through the “full circle of math.”

Learn how Math Monthly combines live group sessions, independent practice, research discussions, and a monthly journal documenting the work. Bring questions about your own understanding and progress as you explore mathematics at your own pace.

Become a member at https://mathmonthly.com to join live Zoom sessions for...

Welcome to Author Jonathan David. Explore mathematics and physics education related to engineering, with discussions on study methods, mathematical reasoning, professional communication, and preparing for college and career opportunities.

Explore memberships at https://authorjond.com for educational lessons, podcasts, fiction, and cooking shows. Join live Zoom sessions for Q&A, guidance, and discussions about studying mathematics and physics.

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The Difference Between Mathematical Theory and the Application of Mathematics

Welcome to Math Monthly. Jonathan David discusses the distinction between developing mathematical theory and applying mathematics to practical problems, emphasizing assumptions, models, and verification.

Every other video I make is for members at https://mathmonthly.com/ — please become a member to access the full library.

Become a member to join my live Zoom sessions for Q&A, guidance, and research participation, with opportunities to receive credit in published books for your contributions.

Lesson 1 | How to Study | LaTeX in Microsoft Word vs. TeXShop

Welcome to Math Monthly. Jonathan David explains the difference between using LaTeX-style equation input in Microsoft Word and writing LaTeX documents in TeXShop, with a focus on preparing mathematical work.

Every other video I make is for members at https://mathmonthly.com/ — please become a member to access the full library.

Become a member to join my live Zoom sessions for Q&A, guidance, and research participation, with opportunities to receive credit in published books for your contributions.

Welcome to Math Monthly. Jonathan David discusses building technical skills, research experience, projects, and a professional resume throughout college to pursue competitive job offers by senior year.

Every other video I make is for members at https://mathmonthly.com/ — please become a member to access the full library.

Become a member to join my live Zoom sessions for Q&A, guidance, and research participation, with opportunities to receive credit in published books for your contributions.

Welcome to Math Monthly.

Every other video I make is for members at https://mathmonthly.com/ — please become a member to access the full library.

Become a member to join my live Zoom sessions for Q&A, guidance, and research participation, with opportunities to receive credit in published books for your contributions.